Question

if da is perpendicular to ie, then we can immediately conclude that <iad and <dae are right angles <iad = <dae ia=ae <ida=<eda

Explanation:

Step1: Recall the definition of perpendicular lines

Perpendicular lines intersect at a right angle (\(90^{\circ}\)).

Step2: Analyze each option

• For the option “\(\angle IAD\) and \(\angle DAE\) are right angles”: Since \(DA\perp IE\), by the definition of perpendicular lines, \(\angle IAD = 90^{\circ}\) and \(\angle DAE=90^{\circ}\).
• For the option “\(\angle IAD=\angle DAE\)”: Just knowing \(DA\perp IE\) doesn't mean these two angles (which are both right angles) being equal is a non - trivial conclusion. We know they are right angles first.
• For the option “\(IA = AE\)”: Perpendicularity of \(DA\) to \(IE\) doesn't imply that \(A\) is the mid - point of \(IE\) (there is no information about \(DA\) being a median).
• For the option “\(\angle IDA=\angle EDA\)”: Perpendicularity of \(DA\) to \(IE\) doesn't imply that \(DA\) is an angle - bisector of \(\angle IDE\) (no information about \(DI = DE\) to use the SSS or SAS congruence for \(\triangle IDA\) and \(\triangle EDA\)).

Answer:

\(\angle IAD\) and \(\angle DAE\) are right angles